<h2>Problem 237</h2>
<div style="color:#666;font-size:80%;">21 March 2009</div><br />
<div class="problem_content">
<p>Let T(<i>n</i>) be the number of tours over a 4 <img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' /> <i>n</i> playing board such that:</p>
<ul>
<li>The tour starts in the top left corner.</li>
<li>The tour consists of moves that are up, down, left, or right one square.</li>
<li>The tour visits each square exactly once.</li>
<li>The tour ends in the bottom left corner.</li>
</ul>

<p>The diagram shows one tour over a 4 <img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' /> 10 board:</p>

<div style="text-align:center;">
<img src="project/images/p_237.gif" alt="" /></div>

<p>T(10) is 2329. What is T(10<img src="" style="display:none;" alt="^(" /><sup>12</sup><img src="" style="display:none;" alt=")" />) modulo 10<img src="" style="display:none;" alt="^(" /><sup>8</sup><img src="" style="display:none;" alt=")" />?</p>
</div><br />
